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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 01:00, 23 February 2013
, 01:00, 23 February 2013→6.36. Irreducibly Triadic Relations: markup
The corresponding projections of <math>\operatorname{Proj}^{(2)} L_0\!</math> and <math>\operatorname{Proj}^{(2)} L_1\!</math> are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of <math>\mathbb{B} \times \mathbb{B}\!</math> and expressed by the universal constant proposition <math>1 : \mathbb{B} \times \mathbb{B} \to \mathbb{B}.\!</math> In summary:
The corresponding projections of <math>\operatorname{Proj}^{(2)} L_0\!</math> and <math>\operatorname{Proj}^{(2)} L_1\!</math> are identical. In fact, all six projections, taken at the level of logical abstraction, constitute precisely the same dyadic relation, isomorphic to the whole of <math>\mathbb{B} \times \mathbb{B}\!</math> and expressed by the universal constant proposition <math>1 : \mathbb{B} \times \mathbb{B} \to \mathbb{B}.\!</math> In summary:
<pre>
{| align="center" cellspacing="8" width="90%"
|
<math>\begin{array}{lllll}
(L_0)_{12} & = & (L_1)_{12} & \cong & \mathbb{B}^2
\\[4pt]
(L_0)_{13} & = & (L_1)_{13} & \cong & \mathbb{B}^2
\\[4pt]
(L_0)_{23} & = & (L_1)_{23} & \cong & \mathbb{B}^2
\end{array}</math>
|}
Thus, R0 and R1 are both examples of irreducibly triadic relations.
Thus, <math>L_0\!</math> and <math>L_1\!</math> are both examples of irreducibly triadic relations.
===6.37. Propositional Types===
===6.37. Propositional Types===